What is moonshine? 
Proceedings of the International Congress of Mathematicians, Vol. I 
(Berlin, 1998). Doc. Math. 1998, Extra Vol. I, 607-615 

Richard E. Borcherds, 
D.P.M.M.S., 16 Mill Lane, Cambridge, CB2 1SB, England. 
home page: www.dpmms.cam.ac.uk/~reb 

This is an informal write up of my talk at the I.C.M. in Berlin. It gives 
some background to Goddard's talk [Go] about the moonshine conjectures. For 
other survey talks about similar topics see [B94], [B98], [LZ], [J], [Ge], 
[Y].